What Lee said - but initially you will need or should have:
1. A good range rod for cleaning with a T handle
2. Appropriate size cleaning jag
3. Appropriate size bronze or nylon bore brush
4. Patches
5. Quality gun oil

With the above items you can consider yourself ready to clean if you use the hot soapy/water and clean water flush method.
Otherwise you will need a good black powder or BP substitute cleaning solvent like T/C's #13 or #17 or a commercial product like windex.

Another item that may come in handy is a patch puller (worm) just in case a patch ever comes off in the bore while you are cleaning.